In this lesson, students recognize the need to find an unknown exponent in an exponential expression or equation. First, students are given a visual pattern that shows a geometric sequence and asked to find where in the sequence that a certain value can be found. Then, students use an exponential model for population growth to estimate when the population will reach certain values.

An optional practice activity prompts students to find the exponent for an expression of the form or that would result in a given value.

To find the values of exponents, students must make sense of the problem and persevere in finding an estimate for the values (MP1).

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.